Neuro-Fuzzy Support for Problem-Solving Environments: A Step Toward Automated Solution of PDEs

  • Authors:
  • Anupam Joshi;Sanjiva Weerawarana;Narendran Ramakrishnan;Elias N. Houstis;John R. Rice

  • Affiliations:
  • -;-;-;-;-

  • Venue:
  • IEEE Computational Science & Engineering
  • Year:
  • 1996

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Abstract

Many scientists and engineers could be using computation in their work to great advantage but aren't. Why is this? Well, largely for the same reasons that even some experienced computational scientists aren't yet using wavelets, or neural networks, or perhaps parallel programming, even if these methods could help them. They simply might not know very much about the techniques, and they're often too busy to learn. This points up the need for problem-solving environments, or PSEs--high-level systems that give a worker in some application area comprehensive and powerful computational assistance while hiding the low-level detail as much as possible. Purdue is a center of research on how to build these tools of the future, some of which are already in use. The authors describe Pythia, an "intelligent assistant" they are incorporating into several PSEs that are designed for solving partial differential equations. Pythia uses a knowledge base to help choose the methods, grid and other parameters, and machines best suited to solving a particular PDE problem. To do this, problems must first be grouped into categories with similar characteristics, and matched against similar problems in the database for which good solution methods are known. The abilities of various neural-network methods to do this classification are compared here. Feedforward multilayer perceptrons trained with enhanced variations of backpropagation, and a neuro-fuzzy method as improved by this team, did especially well and outperformed a traditional non-neural technique.